Sadly that is not the case: in Java 7, javafx is *not* officially part of the JRE, and *not* on the default classpath of `java` or `javac`, so you always have to add it manually. It is just distributed *with* the JRE, as an extra, but that's it. That's probably the thing people complained the most about in javafx 2.x...
And since it is not packaged with *all* versions of java 7 (only above u2), and, even worse, the packaged version changed over time (new non-forward compatible update in u6), the only solution on java 7 is to require your developers to check their version of java, possibly download javafx or update java, and then manually add it to the classpath, one way or another (and for distribution of your app you have to bundle it or use javafxpackager to take care of that).
IntelliJ probably looks into the JDK home you provide and adds it to the classpath, I suppose. That's useful, but dangerous because it makes you believe it is automatically there.
So basically javafx on java 7 is a mess. With java 8 however, it moved to jre/lib/ext [1], so it is on the default classpath of everything, including SBT, and everybody is happy (I use sbt to build a javafx 8 app and it works fine).
I don't have much experience with that, but you could try and locate JDK_HOME, look into "jre/lib/" for the javafx jar, and add it to the classpath or throws an error if missing.